Fast-Projection Methods for the Incompressible Navier–Stokes Equations

Fluids

Gennaro Coppola¹  Francesco Capuano¹  Carlo De Michele¹ 

[1] Dipartimento di Ingegneria Industriale (DII), Università di Napoli “Federico II”, 80125 Napoli, Italy;

关键词: computational fluid dynamics;    incompressible flows;    projection methods;   

DOI  :  10.3390/fluids5040222

来源: DOAJ

【 摘 要 】

An analysis of existing and newly derived fast-projection methods for the numerical integration of incompressible Navier–Stokes equations is proposed. Fast-projection methods are based on the explicit time integration of the semi-discretized Navier–Stokes equations with a Runge–Kutta (RK) method, in which only one Pressure Poisson Equation is solved at each time step. The methods are based on a class of interpolation formulas for the pseudo-pressure computed inside the stages of the RK procedure to enforce the divergence-free constraint on the velocity field. The procedure is independent of the particular multi-stage method, and numerical tests are performed on some of the most commonly employed RK schemes. The proposed methodology includes, as special cases, some fast-projection schemes already presented in the literature. An order-of-accuracy analysis of the family of interpolations here presented reveals that the method generally has second-order accuracy, though it is able to attain third-order accuracy only for specific interpolation schemes. Applications to wall-bounded 2D (driven cavity) and 3D (turbulent channel flow) cases are presented to assess the performances of the schemes in more realistic configurations.

【 授权许可】

Unknown